A Statistical Model For Assessing The Risk Of Subsidence Above Abandoned Mines

A statistical model for assessing the risk of ground subsidence in abandoned mine areas is presented. The model is based on the relationship that exists between .the frequency and the location-of subsidence events in a given area and the physical conditions of the ground. These conditions can be described by a series of geological, mining, and physical variables. The model suggests the existence of regions in the multidimensional space of variables which are associated .with increases or decreases in the frequency of subsidence events. Regions associated with an increase in the frequency of subsidence events correspond to regions of higher risks, and vice versa. Risk assessment is based on the ability to express the limits of these high and low risk regions in the, space of variables, and on the ability to express the degree of membership of blocks of land within any of these regions. The theoretical framework for the model is extracted, from discriminant analysis. Risk is quantified by the probabilities of membership of blocks of land into any of these regions. Risk maps are produced by displaying membership probabilities in. appropriate contouring levels. The model has been applied in two urban areas where subsidence of the ground has been active in the past. The two areas are Penn Hills, near Pittsburgh, and Scranton/Wilkes-Barre in northeastern Pennsylvania. In this paper, only the results for the Scranton/Wilkes-Barre area are presented. Those for the Penn Hills area have been presented elsewhere (Cervantes, et al, 1990). In the- Scranton/Wilkes-Barre area, geostatistical estimates of variables likely to affect the stability of the ground were made using samples from 53 drillholes. The estimates were made for 2000x2000 ft squared blocks of land covering the study area. Discriminant functions were computed from the estimated variables and used to establish regions for classifying blocks of land into one of these two populations: 1) blocks not likely to have a subsidence event, and ii) blocks likely to have one or more subsidence events. The same, discriminant functions were used to compute membership probabilities for blocks of land to tall within any of these two populations. These probabilities were contoured to produce a risk map. The risk map produced compares well with the location of the subsidence events which have occurred to date in the area.